A bag contains 3 white, 5 black and 2 red balls. Two balls are drawn successively without replacement. Find the probability that both drawn balls are black given that the first drawn ball is black.
Answer
The correct answer is — Thus the required probability is 4/9.
Step-by-step solution
- Let B1 be the event that the first ball is black and B2 the event that the second ball is black.
- We are given B1 has occurred, so after removing one black ball the contents are: white=3, black=4, red=2; total remaining balls = 9.
- The conditional probability P(B2|B1) = number of remaining black balls / total remaining balls = 4/9.
- Thus the required probability is 4/9.
Common mistake: Using the original total of 10 balls instead of the reduced total after the first draw.
Concept tested: Conditional probability
Published · How this solution was prepared and checked
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